FIXED RATIO POLYNOMIAL TIME APPROXIMATION ALGORITHM FOR THE PRIZE-COLLECTING ASYMMETRIC TRAVELING SALESMAN PROBLEM

We develop the first fixed-ratio approximation algorithm for the well-known Prize-Collecting Asymmetric Traveling Salesman Problem,  which has numerous valuable applications in operations research. An instance of this problem is given by a complete node- and edge-weighted digraph $G$. Each node of the graph $G$ can either be visited by the resulting route or skipped, for some penalty, while the arcs of $G$  are weighted by non-negative transportation costs that fulfill the triangle inequality constraint. The goal is to find a closed walk that minimizes the total transportation costs augmented by the accumulated penalties. We show that an arbitrary $\alpha$-approximation algorithm for the Asymmetric Traveling Salesman Problem induces an $(\alpha+1)$-approximation for the problem in question. In particular, using the recent $(22+\varepsilon)$-approximation algorithm of V. Traub and J. Vygen that improves the seminal result of  O. Svensson, J. Tarnavski, and L. Végh,  we obtain $(23+\varepsilon)$-approximate solutions for the problem

The Effect of R&D subsidies on private R&D: Evidence from italian manufacturing data

This paper uses a comprehensive firm level data set for the manufacturing sector in Italy to investigate the effect of government support on privately financed R&D expenditure. Estimates from a two-step equation model suggest that public assistance has a positive effect on private R&D investment. A non parametric matching procedure is also used to investigate the same effect. Here again the results suggest that the recipient firms achieve more private R &D than they would have without public support. The paper also examines whether public funding effects the financial sources available for R&D and finds that grants encourage credit financing for R&D. The effects on the use of internal sources are not conclusive

On Approximability of Bounded Degree Instances of Selected Optimization Problems

In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for the restricted version of the problem with improved performance guarantees. In this thesis, we investigate the approximation complexity of selected NP-hard optimization problems restricted to instances with bounded degree, occurrence or weight parameter. Specifically, we consider the family of dense instances, where typically the average degree is bounded from below by some function of the size of the instance. Complementarily, we examine the family of sparse instances, in which the average degree is bounded from above by some fixed constant. We focus on developing new methods for proving explicit approximation hardness results for general as well as for restricted instances. The fist part of the thesis contributes to the systematic investigation of the VERTEX COVER problem in k-hypergraphs and k-partite k-hypergraphs with density and regularity constraints. We design efficient approximation algorithms for the problems with improved performance guarantees as compared to the general case. On the other hand, we prove the optimality of our approximation upper bounds under the Unique Games Conjecture or a variant. In the second part of the thesis, we study mainly the approximation hardness of restricted instances of selected global optimization problems. We establish improved or in some cases the first inapproximability thresholds for the problems considered in this thesis such as the METRIC DIMENSION problem restricted to graphs with maximum degree 3 and the (1,2)-STEINER TREE problem. We introduce a new reductions method for proving explicit approximation lower bounds for problems that are related to the TRAVELING SALESPERSON (TSP) problem. In particular, we prove the best up to now inapproximability thresholds for the general METRIC TSP problem, the ASYMMETRIC TSP problem, the SHORTEST SUPERSTRING problem, the MAXIMUM TSP problem and TSP problems with bounded metrics

Algoritmos de aproximação para problemas de roteamento e conectividade com múltiplas funções de distância

Orientador: Lehilton Lelis Chaves PedrosaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta dissertação, estudamos algumas generalizações de problemas clássicos de roteamento e conectividade cujas instâncias são compostas por um grafo completo e múltiplas funções de distância. Por exemplo, existe o Problema do Caixeiro Alugador (CaRS), no qual um viajante deseja visitar um conjunto de cidades alugando um ou mais carros disponíveis. Cada carro tem uma função de distância e uma taxa de retorno ao local do aluguel. CaRS é uma generalização do Problema do Caixeiro Viajante (TSP). Nós lidamos com esses problemas usando algoritmos de aproximação, que são algoritmos eficientes que produzem soluções com garantia de qualidade. Neste trabalho, são apresentadas duas abordagens, uma baseada em uma redução linear que preserva o fator de aproximação e outra baseada na construção de instâncias de dois problemas distintos. Os problemas considerados são o Steiner TSP, o Problema do Passeio com Coleta de Prêmios e o Problema da Floresta Restrita. Generalizamos cada um desses problemas considerando múltiplas funções de distância e, para cada um deles, apresentamos um algoritmo de aproximação com fator O(logn), onde n é o número de vértices (cidades). Essas aproximações são assintoticamente ótimas, já que não há algoritmos com fator o(log n), a não ser que P = NPAbstract: In this dissertation, we study some generalizations of classical routing and connectivity problems whose instances are composed of a complete graph and multiple distance functions. As an example, there is the Traveling Car Renter Problem (CaRS) in which a traveler wants to visit a set of cities by renting one or more available cars. Each car is associated to a distance function and a service fee to return to the rental location. CaRS is a generalization of the Traveling Salesman Problem (TSP). We deal with these problems using approximation algorithms which are efficient algorithms that produce solutions with quality guarantee. In this work, two approaches are presented, one based on a linear reduction that preserves the approximation factor and the other based on the construction of instances of two distinct problems. The studied problems are the Steiner TSP, the Profitable Tour Problem, and the Constrained Forest Problem. We generalize these problems by considering multiple distance functions and, for each of them, we present an O(log n)-approximation algorithm, where n is the number of vertices (cities). The factor is asymptotically optimal, since there is no approximation algorithm with factor o(log n) unless P = NPMestradoCiência da ComputaçãoMestra em Ciência da Computação001CAPE

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

‘Pull’ motivation : an activity-based typology of international visitors to New Zealand

Using the push and pull framework, this study examines the relationship between tourist activities in New Zealand and behaviours such as tourist spending, travel style (group vs. independent travel) and length of stay. Data from the International Visitor Survey were analysed for a 19-year period (1997–2015). The findings, based on 62,288 respondents, identified 9 typologies of international visitors over this period. For example, type one visitors are primarily pulled by the nature-based activities offered in New Zealand while type two is pulled by adventure activities. Some of the typologies have activities that overlap reflecting the needs of international visitors. Significant relationships were found between the nine typologies, tourist spending, travel style and length of stay. Implications for destination marketing purposes are highlighted. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group